Thus the truth values would be 0 = 0 = 1 = 1 = 0 and 1. If their truth values are 0, then they get and do not get reversed to 1,Īnd if their truth values are 1, then they get and do not get reversed to 0, Because that the point R = R‘ could mean that the statements meant by the point can neither affirm nor negate themselves The dm camp/scholars meant/intended to show that the point R = R‘ meant the self-contradiction of the assumption of the statement that they tried to disprove. (which is obviously wrong,) could be also justified.
Then it should be meaning that the conjunctions of only the negations such as :ġ) that no n-th digit of a countable real number in the dm table is a,Ģ) that no n-th set is included in itself,ģ) that no n-th statement can tell its own truth-ness,Ĥ) that no n-th statement can tell its own provability, Thus, B = S becomes the expression of the complete collections/conjunctions of all the infinite numbers of the negative forms of all the infinite numbers of possible self-referential statements from among the above 1) – 5).īut if such mathematical object B = S could be justified, There is a mapping from the diagonal onto B = S that reverses the truth values like this:įrom P to P‘: the truth values of the statements meant by P are 0, so P‘ accepts them as a truth = 1 and registers (as a part of B = S) the negative forms of the statements chosen from among the above 1) – 5).įrom Q to Q‘: the truth values of the statements shown by Q are 1, so Q‘ negates/reverses them as a falsehood = 0 and registers (as a part of B = S) the negative forms of the statements from among the above 1) – 5).
I was talking about in the page 4 of our conversation „February 2022“ on the is named/called in the picture: the straight line S. The diagonal line in the picture means the diagonal line in Cantor’s dm and all the other possible self-referential statements:ġ) that the n-th digit of a countable real number in the dm table is or is not a,Ģ) that the n-th set is or is not included in the n-th set,ģ) that the n-th statement refers or does not refer to its own truth-ness,Ĥ) that the n-th statement says or does not say that it itself is provable, Now, let me tell you what that picture means. of book title: „The Infinity-Theory Classes“.